In models with flavour conservation, each family of fermions of the same electric charge couples to a single Higgs doublet, via the imposition of discrete \(\mathbb {Z}_2\)  [1]}, [2]}
or global U(1) [3]} symmetries. Then, the diagonalization of the \(M_u\)  and \(M_d\)  matrices, e:dudd, is the same as that of matrices \(N_u\)  and \(N_d\)  and
there are no flavour-violating Yukawa interactions mediated by neutral scalars. In general,
though, that will not be the case and FCNCs occur at tree level.
